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//===- ScalarEvolutionExpander.cpp - Scalar Evolution Analysis ------------===//
// The LLVM Compiler Infrastructure
// This file is distributed under the University of Illinois Open Source
// License. See LICENSE.TXT for details.
// This file contains the implementation of the scalar evolution expander,
// which is used to generate the code corresponding to a given scalar evolution
// expression.
#include "llvm/Analysis/ScalarEvolutionExpander.h"
#include "llvm/ADT/STLExtras.h"
#include "llvm/ADT/SmallSet.h"
#include "llvm/Analysis/InstructionSimplify.h"
#include "llvm/Analysis/LoopInfo.h"
#include "llvm/Analysis/TargetTransformInfo.h"
#include "llvm/IR/DataLayout.h"
#include "llvm/IR/Dominators.h"
#include "llvm/IR/IntrinsicInst.h"
#include "llvm/IR/LLVMContext.h"
#include "llvm/IR/Module.h"
#include "llvm/IR/PatternMatch.h"
#include "llvm/Support/Debug.h"
#include "llvm/Support/raw_ostream.h"
using namespace llvm;
using namespace PatternMatch;
/// ReuseOrCreateCast - Arrange for there to be a cast of V to Ty at IP,
/// reusing an existing cast if a suitable one exists, moving an existing
/// cast if a suitable one exists but isn't in the right place, or
/// creating a new one.
Value *SCEVExpander::ReuseOrCreateCast(Value *V, Type *Ty,
Instruction::CastOps Op,
BasicBlock::iterator IP) {
// This function must be called with the builder having a valid insertion
// point. It doesn't need to be the actual IP where the uses of the returned
// cast will be added, but it must dominate such IP.
// We use this precondition to produce a cast that will dominate all its
// uses. In particular, this is crucial for the case where the builder's
// insertion point *is* the point where we were asked to put the cast.
// Since we don't know the builder's insertion point is actually
// where the uses will be added (only that it dominates it), we are
// not allowed to move it.
BasicBlock::iterator BIP = Builder.GetInsertPoint();
Instruction *Ret = nullptr;
// Check to see if there is already a cast!
for (User *U : V->users())
if (U->getType() == Ty)
if (CastInst *CI = dyn_cast<CastInst>(U))
if (CI->getOpcode() == Op) {
// If the cast isn't where we want it, create a new cast at IP.
// Likewise, do not reuse a cast at BIP because it must dominate
// instructions that might be inserted before BIP.
if (BasicBlock::iterator(CI) != IP || BIP == IP) {
// Create a new cast, and leave the old cast in place in case
// it is being used as an insert point. Clear its operand
// so that it doesn't hold anything live.
Ret = CastInst::Create(Op, V, Ty, "", &*IP);
CI->setOperand(0, UndefValue::get(V->getType()));
Ret = CI;
// Create a new cast.
if (!Ret)
Ret = CastInst::Create(Op, V, Ty, V->getName(), &*IP);
// We assert at the end of the function since IP might point to an
// instruction with different dominance properties than a cast
// (an invoke for example) and not dominate BIP (but the cast does).
assert(SE.DT.dominates(Ret, &*BIP));
return Ret;
static BasicBlock::iterator findInsertPointAfter(Instruction *I,
BasicBlock *MustDominate) {
BasicBlock::iterator IP = ++I->getIterator();
if (auto *II = dyn_cast<InvokeInst>(I))
IP = II->getNormalDest()->begin();
while (isa<PHINode>(IP))
if (isa<FuncletPadInst>(IP) || isa<LandingPadInst>(IP)) {
} else if (isa<CatchSwitchInst>(IP)) {
IP = MustDominate->getFirstInsertionPt();
} else {
assert(!IP->isEHPad() && "unexpected eh pad!");
return IP;
/// InsertNoopCastOfTo - Insert a cast of V to the specified type,
/// which must be possible with a noop cast, doing what we can to share
/// the casts.
Value *SCEVExpander::InsertNoopCastOfTo(Value *V, Type *Ty) {
Instruction::CastOps Op = CastInst::getCastOpcode(V, false, Ty, false);
assert((Op == Instruction::BitCast ||
Op == Instruction::PtrToInt ||
Op == Instruction::IntToPtr) &&
"InsertNoopCastOfTo cannot perform non-noop casts!");
assert(SE.getTypeSizeInBits(V->getType()) == SE.getTypeSizeInBits(Ty) &&
"InsertNoopCastOfTo cannot change sizes!");
// Short-circuit unnecessary bitcasts.
if (Op == Instruction::BitCast) {
if (V->getType() == Ty)
return V;
if (CastInst *CI = dyn_cast<CastInst>(V)) {
if (CI->getOperand(0)->getType() == Ty)
return CI->getOperand(0);
// Short-circuit unnecessary inttoptr<->ptrtoint casts.
if ((Op == Instruction::PtrToInt || Op == Instruction::IntToPtr) &&
SE.getTypeSizeInBits(Ty) == SE.getTypeSizeInBits(V->getType())) {
if (CastInst *CI = dyn_cast<CastInst>(V))
if ((CI->getOpcode() == Instruction::PtrToInt ||
CI->getOpcode() == Instruction::IntToPtr) &&
SE.getTypeSizeInBits(CI->getType()) ==
return CI->getOperand(0);
if (ConstantExpr *CE = dyn_cast<ConstantExpr>(V))
if ((CE->getOpcode() == Instruction::PtrToInt ||
CE->getOpcode() == Instruction::IntToPtr) &&
SE.getTypeSizeInBits(CE->getType()) ==
return CE->getOperand(0);
// Fold a cast of a constant.
if (Constant *C = dyn_cast<Constant>(V))
return ConstantExpr::getCast(Op, C, Ty);
// Cast the argument at the beginning of the entry block, after
// any bitcasts of other arguments.
if (Argument *A = dyn_cast<Argument>(V)) {
BasicBlock::iterator IP = A->getParent()->getEntryBlock().begin();
while ((isa<BitCastInst>(IP) &&
isa<Argument>(cast<BitCastInst>(IP)->getOperand(0)) &&
cast<BitCastInst>(IP)->getOperand(0) != A) ||
return ReuseOrCreateCast(A, Ty, Op, IP);
// Cast the instruction immediately after the instruction.
Instruction *I = cast<Instruction>(V);
BasicBlock::iterator IP = findInsertPointAfter(I, Builder.GetInsertBlock());
return ReuseOrCreateCast(I, Ty, Op, IP);
/// InsertBinop - Insert the specified binary operator, doing a small amount
/// of work to avoid inserting an obviously redundant operation.
Value *SCEVExpander::InsertBinop(Instruction::BinaryOps Opcode,
Value *LHS, Value *RHS) {
// Fold a binop with constant operands.
if (Constant *CLHS = dyn_cast<Constant>(LHS))
if (Constant *CRHS = dyn_cast<Constant>(RHS))
return ConstantExpr::get(Opcode, CLHS, CRHS);
// Do a quick scan to see if we have this binop nearby. If so, reuse it.
unsigned ScanLimit = 6;
BasicBlock::iterator BlockBegin = Builder.GetInsertBlock()->begin();
// Scanning starts from the last instruction before the insertion point.
BasicBlock::iterator IP = Builder.GetInsertPoint();
if (IP != BlockBegin) {
for (; ScanLimit; --IP, --ScanLimit) {
// Don't count dbg.value against the ScanLimit, to avoid perturbing the
// generated code.
if (isa<DbgInfoIntrinsic>(IP))
// Conservatively, do not use any instruction which has any of wrap/exact
// flags installed.
// TODO: Instead of simply disable poison instructions we can be clever
// here and match SCEV to this instruction.
auto canGeneratePoison = [](Instruction *I) {
if (isa<OverflowingBinaryOperator>(I) &&
(I->hasNoSignedWrap() || I->hasNoUnsignedWrap()))
return true;
if (isa<PossiblyExactOperator>(I) && I->isExact())
return true;
return false;
if (IP->getOpcode() == (unsigned)Opcode && IP->getOperand(0) == LHS &&
IP->getOperand(1) == RHS && !canGeneratePoison(&*IP))
return &*IP;
if (IP == BlockBegin) break;
// Save the original insertion point so we can restore it when we're done.
DebugLoc Loc = Builder.GetInsertPoint()->getDebugLoc();
SCEVInsertPointGuard Guard(Builder, this);
// Move the insertion point out of as many loops as we can.
while (const Loop *L = SE.LI.getLoopFor(Builder.GetInsertBlock())) {
if (!L->isLoopInvariant(LHS) || !L->isLoopInvariant(RHS)) break;
BasicBlock *Preheader = L->getLoopPreheader();
if (!Preheader) break;
// Ok, move up a level.
// If we haven't found this binop, insert it.
Instruction *BO = cast<Instruction>(Builder.CreateBinOp(Opcode, LHS, RHS));
return BO;
/// FactorOutConstant - Test if S is divisible by Factor, using signed
/// division. If so, update S with Factor divided out and return true.
/// S need not be evenly divisible if a reasonable remainder can be
/// computed.
/// TODO: When ScalarEvolution gets a SCEVSDivExpr, this can be made
/// unnecessary; in its place, just signed-divide Ops[i] by the scale and
/// check to see if the divide was folded.
static bool FactorOutConstant(const SCEV *&S, const SCEV *&Remainder,
const SCEV *Factor, ScalarEvolution &SE,
const DataLayout &DL) {
// Everything is divisible by one.
if (Factor->isOne())
return true;
// x/x == 1.
if (S == Factor) {
S = SE.getConstant(S->getType(), 1);
return true;
// For a Constant, check for a multiple of the given factor.
if (const SCEVConstant *C = dyn_cast<SCEVConstant>(S)) {
// 0/x == 0.
if (C->isZero())
return true;
// Check for divisibility.
if (const SCEVConstant *FC = dyn_cast<SCEVConstant>(Factor)) {
ConstantInt *CI =
ConstantInt::get(SE.getContext(), C->getAPInt().sdiv(FC->getAPInt()));
// If the quotient is zero and the remainder is non-zero, reject
// the value at this scale. It will be considered for subsequent
// smaller scales.
if (!CI->isZero()) {
const SCEV *Div = SE.getConstant(CI);
S = Div;
Remainder = SE.getAddExpr(
Remainder, SE.getConstant(C->getAPInt().srem(FC->getAPInt())));
return true;
// In a Mul, check if there is a constant operand which is a multiple
// of the given factor.
if (const SCEVMulExpr *M = dyn_cast<SCEVMulExpr>(S)) {
// Size is known, check if there is a constant operand which is a multiple
// of the given factor. If so, we can factor it.
const SCEVConstant *FC = cast<SCEVConstant>(Factor);
if (const SCEVConstant *C = dyn_cast<SCEVConstant>(M->getOperand(0)))
if (!C->getAPInt().srem(FC->getAPInt())) {
SmallVector<const SCEV *, 4> NewMulOps(M->op_begin(), M->op_end());
NewMulOps[0] = SE.getConstant(C->getAPInt().sdiv(FC->getAPInt()));
S = SE.getMulExpr(NewMulOps);
return true;
// In an AddRec, check if both start and step are divisible.
if (const SCEVAddRecExpr *A = dyn_cast<SCEVAddRecExpr>(S)) {
const SCEV *Step = A->getStepRecurrence(SE);
const SCEV *StepRem = SE.getConstant(Step->getType(), 0);
if (!FactorOutConstant(Step, StepRem, Factor, SE, DL))
return false;
if (!StepRem->isZero())
return false;
const SCEV *Start = A->getStart();
if (!FactorOutConstant(Start, Remainder, Factor, SE, DL))
return false;
S = SE.getAddRecExpr(Start, Step, A->getLoop(),
return true;
return false;
/// SimplifyAddOperands - Sort and simplify a list of add operands. NumAddRecs
/// is the number of SCEVAddRecExprs present, which are kept at the end of
/// the list.
static void SimplifyAddOperands(SmallVectorImpl<const SCEV *> &Ops,
Type *Ty,
ScalarEvolution &SE) {
unsigned NumAddRecs = 0;
for (unsigned i = Ops.size(); i > 0 && isa<SCEVAddRecExpr>(Ops[i-1]); --i)
// Group Ops into non-addrecs and addrecs.
SmallVector<const SCEV *, 8> NoAddRecs(Ops.begin(), Ops.end() - NumAddRecs);
SmallVector<const SCEV *, 8> AddRecs(Ops.end() - NumAddRecs, Ops.end());
// Let ScalarEvolution sort and simplify the non-addrecs list.
const SCEV *Sum = NoAddRecs.empty() ?
SE.getConstant(Ty, 0) :
// If it returned an add, use the operands. Otherwise it simplified
// the sum into a single value, so just use that.
if (const SCEVAddExpr *Add = dyn_cast<SCEVAddExpr>(Sum))
Ops.append(Add->op_begin(), Add->op_end());
else if (!Sum->isZero())
// Then append the addrecs.
Ops.append(AddRecs.begin(), AddRecs.end());
/// SplitAddRecs - Flatten a list of add operands, moving addrec start values
/// out to the top level. For example, convert {a + b,+,c} to a, b, {0,+,d}.
/// This helps expose more opportunities for folding parts of the expressions
/// into GEP indices.
static void SplitAddRecs(SmallVectorImpl<const SCEV *> &Ops,
Type *Ty,
ScalarEvolution &SE) {
// Find the addrecs.
SmallVector<const SCEV *, 8> AddRecs;
for (unsigned i = 0, e = Ops.size(); i != e; ++i)
while (const SCEVAddRecExpr *A = dyn_cast<SCEVAddRecExpr>(Ops[i])) {
const SCEV *Start = A->getStart();
if (Start->isZero()) break;
const SCEV *Zero = SE.getConstant(Ty, 0);
if (const SCEVAddExpr *Add = dyn_cast<SCEVAddExpr>(Start)) {
Ops[i] = Zero;
Ops.append(Add->op_begin(), Add->op_end());
e += Add->getNumOperands();
} else {
Ops[i] = Start;
if (!AddRecs.empty()) {
// Add the addrecs onto the end of the list.
Ops.append(AddRecs.begin(), AddRecs.end());
// Resort the operand list, moving any constants to the front.
SimplifyAddOperands(Ops, Ty, SE);
/// expandAddToGEP - Expand an addition expression with a pointer type into
/// a GEP instead of using ptrtoint+arithmetic+inttoptr. This helps
/// BasicAliasAnalysis and other passes analyze the result. See the rules
/// for getelementptr vs. inttoptr in
/// for details.
/// Design note: The correctness of using getelementptr here depends on
/// ScalarEvolution not recognizing inttoptr and ptrtoint operators, as
/// they may introduce pointer arithmetic which may not be safely converted
/// into getelementptr.
/// Design note: It might seem desirable for this function to be more
/// loop-aware. If some of the indices are loop-invariant while others
/// aren't, it might seem desirable to emit multiple GEPs, keeping the
/// loop-invariant portions of the overall computation outside the loop.
/// However, there are a few reasons this is not done here. Hoisting simple
/// arithmetic is a low-level optimization that often isn't very
/// important until late in the optimization process. In fact, passes
/// like InstructionCombining will combine GEPs, even if it means
/// pushing loop-invariant computation down into loops, so even if the
/// GEPs were split here, the work would quickly be undone. The
/// LoopStrengthReduction pass, which is usually run quite late (and
/// after the last InstructionCombining pass), takes care of hoisting
/// loop-invariant portions of expressions, after considering what
/// can be folded using target addressing modes.
Value *SCEVExpander::expandAddToGEP(const SCEV *const *op_begin,
const SCEV *const *op_end,
PointerType *PTy,
Type *Ty,
Value *V) {
Type *OriginalElTy = PTy->getElementType();
Type *ElTy = OriginalElTy;
SmallVector<Value *, 4> GepIndices;
SmallVector<const SCEV *, 8> Ops(op_begin, op_end);
bool AnyNonZeroIndices = false;
// Split AddRecs up into parts as either of the parts may be usable
// without the other.
SplitAddRecs(Ops, Ty, SE);
Type *IntPtrTy = DL.getIntPtrType(PTy);
// Descend down the pointer's type and attempt to convert the other
// operands into GEP indices, at each level. The first index in a GEP
// indexes into the array implied by the pointer operand; the rest of
// the indices index into the element or field type selected by the
// preceding index.
for (;;) {
// If the scale size is not 0, attempt to factor out a scale for
// array indexing.
SmallVector<const SCEV *, 8> ScaledOps;
if (ElTy->isSized()) {
const SCEV *ElSize = SE.getSizeOfExpr(IntPtrTy, ElTy);
if (!ElSize->isZero()) {
SmallVector<const SCEV *, 8> NewOps;
for (const SCEV *Op : Ops) {
const SCEV *Remainder = SE.getConstant(Ty, 0);
if (FactorOutConstant(Op, Remainder, ElSize, SE, DL)) {
// Op now has ElSize factored out.
if (!Remainder->isZero())
AnyNonZeroIndices = true;
} else {
// The operand was not divisible, so add it to the list of operands
// we'll scan next iteration.
// If we made any changes, update Ops.
if (!ScaledOps.empty()) {
Ops = NewOps;
SimplifyAddOperands(Ops, Ty, SE);
// Record the scaled array index for this level of the type. If
// we didn't find any operands that could be factored, tentatively
// assume that element zero was selected (since the zero offset
// would obviously be folded away).
Value *Scaled = ScaledOps.empty() ?
Constant::getNullValue(Ty) :
expandCodeFor(SE.getAddExpr(ScaledOps), Ty);
// Collect struct field index operands.
while (StructType *STy = dyn_cast<StructType>(ElTy)) {
bool FoundFieldNo = false;
// An empty struct has no fields.
if (STy->getNumElements() == 0) break;
// Field offsets are known. See if a constant offset falls within any of
// the struct fields.
if (Ops.empty())
if (const SCEVConstant *C = dyn_cast<SCEVConstant>(Ops[0]))
if (SE.getTypeSizeInBits(C->getType()) <= 64) {
const StructLayout &SL = *DL.getStructLayout(STy);
uint64_t FullOffset = C->getValue()->getZExtValue();
if (FullOffset < SL.getSizeInBytes()) {
unsigned ElIdx = SL.getElementContainingOffset(FullOffset);
ConstantInt::get(Type::getInt32Ty(Ty->getContext()), ElIdx));
ElTy = STy->getTypeAtIndex(ElIdx);
Ops[0] =
SE.getConstant(Ty, FullOffset - SL.getElementOffset(ElIdx));
AnyNonZeroIndices = true;
FoundFieldNo = true;
// If no struct field offsets were found, tentatively assume that
// field zero was selected (since the zero offset would obviously
// be folded away).
if (!FoundFieldNo) {
ElTy = STy->getTypeAtIndex(0u);
if (ArrayType *ATy = dyn_cast<ArrayType>(ElTy))
ElTy = ATy->getElementType();
// If none of the operands were convertible to proper GEP indices, cast
// the base to i8* and do an ugly getelementptr with that. It's still
// better than ptrtoint+arithmetic+inttoptr at least.
if (!AnyNonZeroIndices) {
// Cast the base to i8*.
V = InsertNoopCastOfTo(V,
Type::getInt8PtrTy(Ty->getContext(), PTy->getAddressSpace()));
assert(!isa<Instruction>(V) ||
SE.DT.dominates(cast<Instruction>(V), &*Builder.GetInsertPoint()));
// Expand the operands for a plain byte offset.
Value *Idx = expandCodeFor(SE.getAddExpr(Ops), Ty);
// Fold a GEP with constant operands.
if (Constant *CLHS = dyn_cast<Constant>(V))
if (Constant *CRHS = dyn_cast<Constant>(Idx))
return ConstantExpr::getGetElementPtr(Type::getInt8Ty(Ty->getContext()),
// Do a quick scan to see if we have this GEP nearby. If so, reuse it.
unsigned ScanLimit = 6;
BasicBlock::iterator BlockBegin = Builder.GetInsertBlock()->begin();
// Scanning starts from the last instruction before the insertion point.
BasicBlock::iterator IP = Builder.GetInsertPoint();
if (IP != BlockBegin) {
for (; ScanLimit; --IP, --ScanLimit) {
// Don't count dbg.value against the ScanLimit, to avoid perturbing the
// generated code.
if (isa<DbgInfoIntrinsic>(IP))
if (IP->getOpcode() == Instruction::GetElementPtr &&
IP->getOperand(0) == V && IP->getOperand(1) == Idx)
return &*IP;
if (IP == BlockBegin) break;
// Save the original insertion point so we can restore it when we're done.
SCEVInsertPointGuard Guard(Builder, this);
// Move the insertion point out of as many loops as we can.
while (const Loop *L = SE.LI.getLoopFor(Builder.GetInsertBlock())) {
if (!L->isLoopInvariant(V) || !L->isLoopInvariant(Idx)) break;
BasicBlock *Preheader = L->getLoopPreheader();
if (!Preheader) break;
// Ok, move up a level.
// Emit a GEP.
Value *GEP = Builder.CreateGEP(Builder.getInt8Ty(), V, Idx, "uglygep");
return GEP;
SCEVInsertPointGuard Guard(Builder, this);
// Move the insertion point out of as many loops as we can.
while (const Loop *L = SE.LI.getLoopFor(Builder.GetInsertBlock())) {
if (!L->isLoopInvariant(V)) break;
bool AnyIndexNotLoopInvariant = any_of(
GepIndices, [L](Value *Op) { return !L->isLoopInvariant(Op); });
if (AnyIndexNotLoopInvariant)
BasicBlock *Preheader = L->getLoopPreheader();
if (!Preheader) break;
// Ok, move up a level.
// Insert a pretty getelementptr. Note that this GEP is not marked inbounds,
// because ScalarEvolution may have changed the address arithmetic to
// compute a value which is beyond the end of the allocated object.
Value *Casted = V;
if (V->getType() != PTy)
Casted = InsertNoopCastOfTo(Casted, PTy);
Value *GEP = Builder.CreateGEP(OriginalElTy, Casted, GepIndices, "scevgep");
return expand(SE.getAddExpr(Ops));
Value *SCEVExpander::expandAddToGEP(const SCEV *Op, PointerType *PTy, Type *Ty,
Value *V) {
const SCEV *const Ops[1] = {Op};
return expandAddToGEP(Ops, Ops + 1, PTy, Ty, V);
/// PickMostRelevantLoop - Given two loops pick the one that's most relevant for
/// SCEV expansion. If they are nested, this is the most nested. If they are
/// neighboring, pick the later.
static const Loop *PickMostRelevantLoop(const Loop *A, const Loop *B,
DominatorTree &DT) {
if (!A) return B;
if (!B) return A;
if (A->contains(B)) return B;
if (B->contains(A)) return A;
if (DT.dominates(A->getHeader(), B->getHeader())) return B;
if (DT.dominates(B->getHeader(), A->getHeader())) return A;
return A; // Arbitrarily break the tie.
/// getRelevantLoop - Get the most relevant loop associated with the given
/// expression, according to PickMostRelevantLoop.
const Loop *SCEVExpander::getRelevantLoop(const SCEV *S) {
// Test whether we've already computed the most relevant loop for this SCEV.
auto Pair = RelevantLoops.insert(std::make_pair(S, nullptr));
if (!Pair.second)
return Pair.first->second;
if (isa<SCEVConstant>(S))
// A constant has no relevant loops.
return nullptr;
if (const SCEVUnknown *U = dyn_cast<SCEVUnknown>(S)) {
if (const Instruction *I = dyn_cast<Instruction>(U->getValue()))
return Pair.first->second = SE.LI.getLoopFor(I->getParent());
// A non-instruction has no relevant loops.
return nullptr;
if (const SCEVNAryExpr *N = dyn_cast<SCEVNAryExpr>(S)) {
const Loop *L = nullptr;
if (const SCEVAddRecExpr *AR = dyn_cast<SCEVAddRecExpr>(S))
L = AR->getLoop();
for (const SCEV *Op : N->operands())
L = PickMostRelevantLoop(L, getRelevantLoop(Op), SE.DT);
return RelevantLoops[N] = L;
if (const SCEVCastExpr *C = dyn_cast<SCEVCastExpr>(S)) {
const Loop *Result = getRelevantLoop(C->getOperand());
return RelevantLoops[C] = Result;
if (const SCEVUDivExpr *D = dyn_cast<SCEVUDivExpr>(S)) {
const Loop *Result = PickMostRelevantLoop(
getRelevantLoop(D->getLHS()), getRelevantLoop(D->getRHS()), SE.DT);
return RelevantLoops[D] = Result;
llvm_unreachable("Unexpected SCEV type!");
namespace {
/// LoopCompare - Compare loops by PickMostRelevantLoop.
class LoopCompare {
DominatorTree &DT;
explicit LoopCompare(DominatorTree &dt) : DT(dt) {}
bool operator()(std::pair<const Loop *, const SCEV *> LHS,
std::pair<const Loop *, const SCEV *> RHS) const {
// Keep pointer operands sorted at the end.
if (LHS.second->getType()->isPointerTy() !=
return LHS.second->getType()->isPointerTy();
// Compare loops with PickMostRelevantLoop.
if (LHS.first != RHS.first)
return PickMostRelevantLoop(LHS.first, RHS.first, DT) != LHS.first;
// If one operand is a non-constant negative and the other is not,
// put the non-constant negative on the right so that a sub can
// be used instead of a negate and add.
if (LHS.second->isNonConstantNegative()) {
if (!RHS.second->isNonConstantNegative())
return false;
} else if (RHS.second->isNonConstantNegative())
return true;
// Otherwise they are equivalent according to this comparison.
return false;
Value *SCEVExpander::visitAddExpr(const SCEVAddExpr *S) {
Type *Ty = SE.getEffectiveSCEVType(S->getType());
// Collect all the add operands in a loop, along with their associated loops.
// Iterate in reverse so that constants are emitted last, all else equal, and
// so that pointer operands are inserted first, which the code below relies on
// to form more involved GEPs.
SmallVector<std::pair<const Loop *, const SCEV *>, 8> OpsAndLoops;
for (std::reverse_iterator<SCEVAddExpr::op_iterator> I(S->op_end()),
E(S->op_begin()); I != E; ++I)
OpsAndLoops.push_back(std::make_pair(getRelevantLoop(*I), *I));
// Sort by loop. Use a stable sort so that constants follow non-constants and
// pointer operands precede non-pointer operands.
std::stable_sort(OpsAndLoops.begin(), OpsAndLoops.end(), LoopCompare(SE.DT));
// Emit instructions to add all the operands. Hoist as much as possible
// out of loops, and form meaningful getelementptrs where possible.
Value *Sum = nullptr;
for (auto I = OpsAndLoops.begin(), E = OpsAndLoops.end(); I != E;) {
const Loop *CurLoop = I->first;
const SCEV *Op = I->second;
if (!Sum) {
// This is the first operand. Just expand it.
Sum = expand(Op);
} else if (PointerType *PTy = dyn_cast<PointerType>(Sum->getType())) {
// The running sum expression is a pointer. Try to form a getelementptr
// at this level with that as the base.
SmallVector<const SCEV *, 4> NewOps;
for (; I != E && I->first == CurLoop; ++I) {
// If the operand is SCEVUnknown and not instructions, peek through
// it, to enable more of it to be folded into the GEP.
const SCEV *X = I->second;
if (const SCEVUnknown *U = dyn_cast<SCEVUnknown>(X))
if (!isa<Instruction>(U->getValue()))
X = SE.getSCEV(U->getValue());
Sum = expandAddToGEP(NewOps.begin(), NewOps.end(), PTy, Ty, Sum);
} else if (PointerType *PTy = dyn_cast<PointerType>(Op->getType())) {
// The running sum is an integer, and there's a pointer at this level.
// Try to form a getelementptr. If the running sum is instructions,
// use a SCEVUnknown to avoid re-analyzing them.
SmallVector<const SCEV *, 4> NewOps;
NewOps.push_back(isa<Instruction>(Sum) ? SE.getUnknown(Sum) :
for (++I; I != E && I->first == CurLoop; ++I)
Sum = expandAddToGEP(NewOps.begin(), NewOps.end(), PTy, Ty, expand(Op));
} else if (Op->isNonConstantNegative()) {
// Instead of doing a negate and add, just do a subtract.
Value *W = expandCodeFor(SE.getNegativeSCEV(Op), Ty);
Sum = InsertNoopCastOfTo(Sum, Ty);
Sum = InsertBinop(Instruction::Sub, Sum, W);
} else {
// A simple add.
Value *W = expandCodeFor(Op, Ty);
Sum = InsertNoopCastOfTo(Sum, Ty);
// Canonicalize a constant to the RHS.
if (isa<Constant>(Sum)) std::swap(Sum, W);
Sum = InsertBinop(Instruction::Add, Sum, W);
return Sum;
Value *SCEVExpander::visitMulExpr(const SCEVMulExpr *S) {
Type *Ty = SE.getEffectiveSCEVType(S->getType());
// Collect all the mul operands in a loop, along with their associated loops.
// Iterate in reverse so that constants are emitted last, all else equal.
SmallVector<std::pair<const Loop *, const SCEV *>, 8> OpsAndLoops;
for (std::reverse_iterator<SCEVMulExpr::op_iterator> I(S->op_end()),
E(S->op_begin()); I != E; ++I)
OpsAndLoops.push_back(std::make_pair(getRelevantLoop(*I), *I));
// Sort by loop. Use a stable sort so that constants follow non-constants.
std::stable_sort(OpsAndLoops.begin(), OpsAndLoops.end(), LoopCompare(SE.DT));
// Emit instructions to mul all the operands. Hoist as much as possible
// out of loops.
Value *Prod = nullptr;
auto I = OpsAndLoops.begin();
// Expand the calculation of X pow N in the following manner:
// Let N = P1 + P2 + ... + PK, where all P are powers of 2. Then:
// X pow N = (X pow P1) * (X pow P2) * ... * (X pow PK).
const auto ExpandOpBinPowN = [this, &I, &OpsAndLoops, &Ty]() {
auto E = I;
// Calculate how many times the same operand from the same loop is included
// into this power.
uint64_t Exponent = 0;
const uint64_t MaxExponent = UINT64_MAX >> 1;
// No one sane will ever try to calculate such huge exponents, but if we
// need this, we stop on UINT64_MAX / 2 because we need to exit the loop
// below when the power of 2 exceeds our Exponent, and we want it to be
// 1u << 31 at most to not deal with unsigned overflow.
while (E != OpsAndLoops.end() && *I == *E && Exponent != MaxExponent) {
assert(Exponent > 0 && "Trying to calculate a zeroth exponent of operand?");
// Calculate powers with exponents 1, 2, 4, 8 etc. and include those of them
// that are needed into the result.
Value *P = expandCodeFor(I->second, Ty);
Value *Result = nullptr;
if (Exponent & 1)
Result = P;
for (uint64_t BinExp = 2; BinExp <= Exponent; BinExp <<= 1) {
P = InsertBinop(Instruction::Mul, P, P);
if (Exponent & BinExp)
Result = Result ? InsertBinop(Instruction::Mul, Result, P) : P;
I = E;
assert(Result && "Nothing was expanded?");
return Result;
while (I != OpsAndLoops.end()) {
if (!Prod) {
// This is the first operand. Just expand it.
Prod = ExpandOpBinPowN();
} else if (I->second->isAllOnesValue()) {
// Instead of doing a multiply by negative one, just do a negate.
Prod = InsertNoopCastOfTo(Prod, Ty);
Prod = InsertBinop(Instruction::Sub, Constant::getNullValue(Ty), Prod);
} else {
// A simple mul.
Value *W = ExpandOpBinPowN();
Prod = InsertNoopCastOfTo(Prod, Ty);
// Canonicalize a constant to the RHS.
if (isa<Constant>(Prod)) std::swap(Prod, W);
const APInt *RHS;
if (match(W, m_Power2(RHS))) {
// Canonicalize Prod*(1<<C) to Prod<<C.
assert(!Ty->isVectorTy() && "vector types are not SCEVable");
Prod = InsertBinop(Instruction::Shl, Prod,
ConstantInt::get(Ty, RHS->logBase2()));
} else {
Prod = InsertBinop(Instruction::Mul, Prod, W);
return Prod;
Value *SCEVExpander::visitUDivExpr(const SCEVUDivExpr *S) {
Type *Ty = SE.getEffectiveSCEVType(S->getType());
Value *LHS = expandCodeFor(S->getLHS(), Ty);
if (const SCEVConstant *SC = dyn_cast<SCEVConstant>(S->getRHS())) {
const APInt &RHS = SC->getAPInt();
if (RHS.isPowerOf2())
return InsertBinop(Instruction::LShr, LHS,
ConstantInt::get(Ty, RHS.logBase2()));
Value *RHS = expandCodeFor(S->getRHS(), Ty);
return InsertBinop(Instruction::UDiv, LHS, RHS);
/// Move parts of Base into Rest to leave Base with the minimal
/// expression that provides a pointer operand suitable for a
/// GEP expansion.
static void ExposePointerBase(const SCEV *&Base, const SCEV *&Rest,
ScalarEvolution &SE) {
while (const SCEVAddRecExpr *A = dyn_cast<SCEVAddRecExpr>(Base)) {
Base = A->getStart();
Rest = SE.getAddExpr(Rest,
SE.getAddRecExpr(SE.getConstant(A->getType(), 0),
if (const SCEVAddExpr *A = dyn_cast<SCEVAddExpr>(Base)) {
Base = A->getOperand(A->getNumOperands()-1);
SmallVector<const SCEV *, 8> NewAddOps(A->op_begin(), A->op_end());
NewAddOps.back() = Rest;
Rest = SE.getAddExpr(NewAddOps);
ExposePointerBase(Base, Rest, SE);
/// Determine if this is a well-behaved chain of instructions leading back to
/// the PHI. If so, it may be reused by expanded expressions.
bool SCEVExpander::isNormalAddRecExprPHI(PHINode *PN, Instruction *IncV,
const Loop *L) {
if (IncV->getNumOperands() == 0 || isa<PHINode>(IncV) ||
(isa<CastInst>(IncV) && !isa<BitCastInst>(IncV)))
return false;
// If any of the operands don't dominate the insert position, bail.
// Addrec operands are always loop-invariant, so this can only happen
// if there are instructions which haven't been hoisted.
if (L == IVIncInsertLoop) {
for (User::op_iterator OI = IncV->op_begin()+1,
OE = IncV->op_end(); OI != OE; ++OI)
if (Instruction *OInst = dyn_cast<Instruction>(OI))
if (!SE.DT.dominates(OInst, IVIncInsertPos))
return false;
// Advance to the next instruction.
IncV = dyn_cast<Instruction>(IncV->getOperand(0));
if (!IncV)
return false;
if (IncV->mayHaveSideEffects())
return false;
if (IncV == PN)
return true;
return isNormalAddRecExprPHI(PN, IncV, L);
/// getIVIncOperand returns an induction variable increment's induction
/// variable operand.
/// If allowScale is set, any type of GEP is allowed as long as the nonIV
/// operands dominate InsertPos.
/// If allowScale is not set, ensure that a GEP increment conforms to one of the
/// simple patterns generated by getAddRecExprPHILiterally and
/// expandAddtoGEP. If the pattern isn't recognized, return NULL.
Instruction *SCEVExpander::getIVIncOperand(Instruction *IncV,
Instruction *InsertPos,
bool allowScale) {
if (IncV == InsertPos)
return nullptr;
switch (IncV->getOpcode()) {
return nullptr;
// Check for a simple Add/Sub or GEP of a loop invariant step.
case Instruction::Add:
case Instruction::Sub: {
Instruction *OInst = dyn_cast<Instruction>(IncV->getOperand(1));
if (!OInst || SE.DT.dominates(OInst, InsertPos))
return dyn_cast<Instruction>(IncV->getOperand(0));
return nullptr;
case Instruction::BitCast:
return dyn_cast<Instruction>(IncV->getOperand(0));
case Instruction::GetElementPtr:
for (auto I = IncV->op_begin() + 1, E = IncV->op_end(); I != E; ++I) {
if (isa<Constant>(*I))
if (Instruction *OInst = dyn_cast<Instruction>(*I)) {
if (!SE.DT.dominates(OInst, InsertPos))
return nullptr;
if (allowScale) {
// allow any kind of GEP as long as it can be hoisted.
// This must be a pointer addition of constants (pretty), which is already
// handled, or some number of address-size elements (ugly). Ugly geps
// have 2 operands. i1* is used by the expander to represent an
// address-size element.
if (IncV->getNumOperands() != 2)
return nullptr;
unsigned AS = cast<PointerType>(IncV->getType())->getAddressSpace();
if (IncV->getType() != Type::getInt1PtrTy(SE.getContext(), AS)
&& IncV->getType() != Type::getInt8PtrTy(SE.getContext(), AS))
return nullptr;
return dyn_cast<Instruction>(IncV->getOperand(0));
/// If the insert point of the current builder or any of the builders on the
/// stack of saved builders has 'I' as its insert point, update it to point to
/// the instruction after 'I'. This is intended to be used when the instruction
/// 'I' is being moved. If this fixup is not done and 'I' is moved to a
/// different block, the inconsistent insert point (with a mismatched
/// Instruction and Block) can lead to an instruction being inserted in a block
/// other than its parent.
void SCEVExpander::fixupInsertPoints(Instruction *I) {
BasicBlock::iterator It(*I);
BasicBlock::iterator NewInsertPt = std::next(It);
if (Builder.GetInsertPoint() == It)
for (auto *InsertPtGuard : InsertPointGuards)
if (InsertPtGuard->GetInsertPoint() == It)
/// hoistStep - Attempt to hoist a simple IV increment above InsertPos to make
/// it available to other uses in this loop. Recursively hoist any operands,
/// until we reach a value that dominates InsertPos.
bool SCEVExpander::hoistIVInc(Instruction *IncV, Instruction *InsertPos) {
if (SE.DT.dominates(IncV, InsertPos))
return true;
// InsertPos must itself dominate IncV so that IncV's new position satisfies
// its existing users.
if (isa<PHINode>(InsertPos) ||
!SE.DT.dominates(InsertPos->getParent(), IncV->getParent()))
return false;
if (!SE.LI.movementPreservesLCSSAForm(IncV, InsertPos))
return false;
// Check that the chain of IV operands leading back to Phi can be hoisted.
SmallVector<Instruction*, 4> IVIncs;
for(;;) {
Instruction *Oper = getIVIncOperand(IncV, InsertPos, /*allowScale*/true);
if (!Oper)
return false;
// IncV is safe to hoist.
IncV = Oper;
if (SE.DT.dominates(IncV, InsertPos))
for (auto I = IVIncs.rbegin(), E = IVIncs.rend(); I != E; ++I) {
return true;
/// Determine if this cyclic phi is in a form that would have been generated by
/// LSR. We don't care if the phi was actually expanded in this pass, as long
/// as it is in a low-cost form, for example, no implied multiplication. This
/// should match any patterns generated by getAddRecExprPHILiterally and
/// expandAddtoGEP.
bool SCEVExpander::isExpandedAddRecExprPHI(PHINode *PN, Instruction *IncV,
const Loop *L) {
for(Instruction *IVOper = IncV;
(IVOper = getIVIncOperand(IVOper, L->getLoopPreheader()->getTerminator(),
/*allowScale=*/false));) {
if (IVOper == PN)
return true;
return false;
/// expandIVInc - Expand an IV increment at Builder's current InsertPos.
/// Typically this is the LatchBlock terminator or IVIncInsertPos, but we may
/// need to materialize IV increments elsewhere to handle difficult situations.
Value *SCEVExpander::expandIVInc(PHINode *PN, Value *StepV, const Loop *L,
Type *ExpandTy, Type *IntTy,
bool useSubtract) {
Value *IncV;
// If the PHI is a pointer, use a GEP, otherwise use an add or sub.
if (ExpandTy->isPointerTy()) {
PointerType *GEPPtrTy = cast<PointerType>(ExpandTy);
// If the step isn't constant, don't use an implicitly scaled GEP, because
// that would require a multiply inside the loop.
if (!isa<ConstantInt>(StepV))
GEPPtrTy = PointerType::get(Type::getInt1Ty(SE.getContext()),
IncV = expandAddToGEP(SE.getSCEV(StepV), GEPPtrTy, IntTy, PN);
if (IncV->getType() != PN->getType()) {
IncV = Builder.CreateBitCast(IncV, PN->getType());
} else {
IncV = useSubtract ?
Builder.CreateSub(PN, StepV, Twine(IVName) + "") :
Builder.CreateAdd(PN, StepV, Twine(IVName) + "");
return IncV;
/// Hoist the addrec instruction chain rooted in the loop phi above the
/// position. This routine assumes that this is possible (has been checked).
void SCEVExpander::hoistBeforePos(DominatorTree *DT, Instruction *InstToHoist,
Instruction *Pos, PHINode *LoopPhi) {
do {
if (DT->dominates(InstToHoist, Pos))
// Make sure the increment is where we want it. But don't move it
// down past a potential existing post-inc user.
Pos = InstToHoist;
InstToHoist = cast<Instruction>(InstToHoist->getOperand(0));
} while (InstToHoist != LoopPhi);
/// Check whether we can cheaply express the requested SCEV in terms of
/// the available PHI SCEV by truncation and/or inversion of the step.
static bool canBeCheaplyTransformed(ScalarEvolution &SE,
const SCEVAddRecExpr *Phi,
const SCEVAddRecExpr *Requested,
bool &InvertStep) {
Type *PhiTy = SE.getEffectiveSCEVType(Phi->getType());
Type *RequestedTy = SE.getEffectiveSCEVType(Requested->getType());
if (RequestedTy->getIntegerBitWidth() > PhiTy->getIntegerBitWidth())
return false;
// Try truncate it if necessary.
Phi = dyn_cast<SCEVAddRecExpr>(SE.getTruncateOrNoop(Phi, RequestedTy));
if (!Phi)
return false;
// Check whether truncation will help.
if (Phi == Requested) {
InvertStep = false;
return true;
// Check whether inverting will help: {R,+,-1} == R - {0,+,1}.
if (SE.getAddExpr(Requested->getStart(),
SE.getNegativeSCEV(Requested)) == Phi) {
InvertStep = true;
return true;
return false;
static bool IsIncrementNSW(ScalarEvolution &SE, const SCEVAddRecExpr *AR) {
if (!isa<IntegerType>(AR->getType()))
return false;
unsigned BitWidth = cast<IntegerType>(AR->getType())->getBitWidth();
Type *WideTy = IntegerType::get(AR->getType()->getContext(), BitWidth * 2);
const SCEV *Step = AR->getStepRecurrence(SE);
const SCEV *OpAfterExtend = SE.getAddExpr(SE.getSignExtendExpr(Step, WideTy),
SE.getSignExtendExpr(AR, WideTy));
const SCEV *ExtendAfterOp =
SE.getSignExtendExpr(SE.getAddExpr(AR, Step), WideTy);
return ExtendAfterOp == OpAfterExtend;
static bool IsIncrementNUW(ScalarEvolution &SE, const SCEVAddRecExpr *AR) {
if (!isa<IntegerType>(AR->getType()))
return false;
unsigned BitWidth = cast<IntegerType>(AR->getType())->getBitWidth();
Type *WideTy = IntegerType::get(AR->getType()->getContext(), BitWidth * 2);
const SCEV *Step = AR->getStepRecurrence(SE);
const SCEV *OpAfterExtend = SE.getAddExpr(SE.getZeroExtendExpr(Step, WideTy),
SE.getZeroExtendExpr(AR, WideTy));
const SCEV *ExtendAfterOp =
SE.getZeroExtendExpr(SE.getAddExpr(AR, Step), WideTy);
return ExtendAfterOp == OpAfterExtend;
/// getAddRecExprPHILiterally - Helper for expandAddRecExprLiterally. Expand
/// the base addrec, which is the addrec without any non-loop-dominating
/// values, and return the PHI.
PHINode *
SCEVExpander::getAddRecExprPHILiterally(const SCEVAddRecExpr *Normalized,
const Loop *L,
Type *ExpandTy,
Type *IntTy,
Type *&TruncTy,
bool &InvertStep) {
assert((!IVIncInsertLoop||IVIncInsertPos) && "Uninitialized insert position");
// Reuse a previously-inserted PHI, if present.
BasicBlock *LatchBlock = L->getLoopLatch();
if (LatchBlock) {
PHINode *AddRecPhiMatch = nullptr;
Instruction *IncV = nullptr;
TruncTy = nullptr;
InvertStep = false;
// Only try partially matching scevs that need truncation and/or
// step-inversion if we know this loop is outside the current loop.
bool TryNonMatchingSCEV =
IVIncInsertLoop &&
SE.DT.properlyDominates(LatchBlock, IVIncInsertLoop->getHeader());
for (PHINode &PN : L->getHeader()->phis()) {
if (!SE.isSCEVable(PN.getType()))
const SCEVAddRecExpr *PhiSCEV = dyn_cast<SCEVAddRecExpr>(SE.getSCEV(&PN));
if (!PhiSCEV)
bool IsMatchingSCEV = PhiSCEV == Normalized;
// We only handle truncation and inversion of phi recurrences for the
// expanded expression if the expanded expression's loop dominates the
// loop we insert to. Check now, so we can bail out early.
if (!IsMatchingSCEV && !TryNonMatchingSCEV)
// TODO: this possibly can be reworked to avoid this cast at all.
Instruction *TempIncV =
if (!TempIncV)
// Check whether we can reuse this PHI node.
if (LSRMode) {
if (!isExpandedAddRecExprPHI(&PN, TempIncV, L))
if (L == IVIncInsertLoop && !hoistIVInc(TempIncV, IVIncInsertPos))
} else {
if (!isNormalAddRecExprPHI(&PN, TempIncV, L))
// Stop if we have found an exact match SCEV.
if (IsMatchingSCEV) {
IncV = TempIncV;
TruncTy = nullptr;
InvertStep = false;
AddRecPhiMatch = &PN;
// Try whether the phi can be translated into the requested form
// (truncated and/or offset by a constant).
if ((!TruncTy || InvertStep) &&
canBeCheaplyTransformed(SE, PhiSCEV, Normalized, InvertStep)) {
// Record the phi node. But don't stop we might find an exact match
// later.
AddRecPhiMatch = &PN;
IncV = TempIncV;
TruncTy = SE.getEffectiveSCEVType(Normalized->getType());
if (AddRecPhiMatch) {
// Potentially, move the increment. We have made sure in
// isExpandedAddRecExprPHI or hoistIVInc that this is possible.
if (L == IVIncInsertLoop)
hoistBeforePos(&SE.DT, IncV, IVIncInsertPos, AddRecPhiMatch);
// Ok, the add recurrence looks usable.
// Remember this PHI, even in post-inc mode.
// Remember the increment.
return AddRecPhiMatch;
// Save the original insertion point so we can restore it when we're done.
SCEVInsertPointGuard Guard(Builder, this);
// Another AddRec may need to be recursively expanded below. For example, if
// this AddRec is quadratic, the StepV may itself be an AddRec in this
// loop. Remove this loop from the PostIncLoops set before expanding such
// AddRecs. Otherwise, we cannot find a valid position for the step
// (i.e. StepV can never dominate its loop header). Ideally, we could do
// SavedIncLoops.swap(PostIncLoops), but we generally have a single element,
// so it's not worth implementing SmallPtrSet::swap.
PostIncLoopSet SavedPostIncLoops = PostIncLoops;
// Expand code for the start value into the loop preheader.
assert(L->getLoopPreheader() &&
"Can't expand add recurrences without a loop preheader!");
Value *StartV = expandCodeFor(Normalized->getStart(), ExpandTy,
// StartV must have been be inserted into L's preheader to dominate the new
// phi.
assert(!isa<Instruction>(StartV) ||
// Expand code for the step value. Do this before creating the PHI so that PHI
// reuse code doesn't see an incomplete PHI.
const SCEV *Step = Normalized->getStepRecurrence(SE);
// If the stride is negative, insert a sub instead of an add for the increment
// (unless it's a constant, because subtracts of constants are canonicalized
// to adds).
bool useSubtract = !ExpandTy->isPointerTy() && Step->isNonConstantNegative();
if (useSubtract)
Step = SE.getNegativeSCEV(Step);
// Expand the step somewhere that dominates the loop header.
Value *StepV = expandCodeFor(Step, IntTy, &L->getHeader()->front());
// The no-wrap behavior proved by IsIncrement(NUW|NSW) is only applicable if
// we actually do emit an addition. It does not apply if we emit a
// subtraction.
bool IncrementIsNUW = !useSubtract && IsIncrementNUW(SE, Normalized);
bool IncrementIsNSW = !useSubtract && IsIncrementNSW(SE, Normalized);
// Create the PHI.
BasicBlock *Header = L->getHeader();
Builder.SetInsertPoint(Header, Header->begin());
pred_iterator HPB = pred_begin(Header), HPE = pred_end(Header);
PHINode *PN = Builder.CreatePHI(ExpandTy, std::distance(HPB, HPE),
Twine(IVName) + ".iv");
// Create the step instructions and populate the PHI.
for (pred_iterator HPI = HPB; HPI != HPE; ++HPI) {
BasicBlock *Pred = *HPI;
// Add a start value.
if (!L->contains(Pred)) {
PN->addIncoming(StartV, Pred);
// Create a step value and add it to the PHI.
// If IVIncInsertLoop is non-null and equal to the addrec's loop, insert the
// instructions at IVIncInsertPos.
Instruction *InsertPos = L == IVIncInsertLoop ?
IVIncInsertPos : Pred->getTerminator();
Value *IncV = expandIVInc(PN, StepV, L, ExpandTy, IntTy, useSubtract);
if (isa<OverflowingBinaryOperator>(IncV)) {
if (IncrementIsNUW)
if (IncrementIsNSW)
PN->addIncoming(IncV, Pred);
// After expanding subexpressions, restore the PostIncLoops set so the caller
// can ensure that IVIncrement dominates the current uses.
PostIncLoops = SavedPostIncLoops;
// Remember this PHI, even in post-inc mode.
return PN;
Value *SCEVExpander::expandAddRecExprLiterally(const SCEVAddRecExpr *S) {
Type *STy = S->getType();
Type *IntTy = SE.getEffectiveSCEVType(STy);
const Loop *L = S->getLoop();
// Determine a normalized form of this expression, which is the expression
// before any post-inc adjustment is made.
const SCEVAddRecExpr *Normalized = S;
if (PostIncLoops.count(L)) {
PostIncLoopSet Loops;
Normalized = cast<SCEVAddRecExpr>(normalizeForPostIncUse(S, Loops, SE));
// Strip off any non-loop-dominating component from the addrec start.
const SCEV *Start = Normalized->getStart();
const SCEV *PostLoopOffset = nullptr;
if (!SE.properlyDominates(Start, L->getHeader())) {
PostLoopOffset = Start;
Start = SE.getConstant(Normalized->getType(), 0);
Normalized = cast<SCEVAddRecExpr>(
SE.getAddRecExpr(Start, Normalized->getStepRecurrence(SE),
// Strip off any non-loop-dominating component from the addrec step.
const SCEV *Step = Normalized->getStepRecurrence(SE);
const SCEV *PostLoopScale = nullptr;
if (!SE.dominates(Step, L->getHeader())) {
PostLoopScale = Step;
Step = SE.getConstant(Normalized->getType(), 1);
if (!Start->isZero()) {
// The normalization below assumes that Start is constant zero, so if
// it isn't re-associate Start to PostLoopOffset.
assert(!PostLoopOffset && "Start not-null but PostLoopOffset set?");
PostLoopOffset = Start;
Start = SE.getConstant(Normalized->getType(), 0);
Normalized =
Start, Step, Normalized->getLoop(),
// Expand the core addrec. If we need post-loop scaling, force it to
// expand to an integer type to avoid the need for additional casting.
Type *ExpandTy = PostLoopScale ? IntTy : STy;
// We can't use a pointer type for the addrec if the pointer type is
// non-integral.
Type *AddRecPHIExpandTy =
DL.isNonIntegralPointerType(STy) ? Normalized->getType() : ExpandTy;
// In some cases, we decide to reuse an existing phi node but need to truncate
// it and/or invert the step.
Type *TruncTy = nullptr;
bool InvertStep = false;
PHINode *PN = getAddRecExprPHILiterally(Normalized, L, AddRecPHIExpandTy,
IntTy, TruncTy, InvertStep);
// Accommodate post-inc mode, if necessary.
Value *Result;
if (!PostIncLoops.count(L))
Result = PN;
else {
// In PostInc mode, use the post-incremented value.
BasicBlock *LatchBlock = L->getLoopLatch();
assert(LatchBlock && "PostInc mode requires a unique loop latch!");
Result = PN->getIncomingValueForBlock(LatchBlock);
// For an expansion to use the postinc form, the client must call
// expandCodeFor with an InsertPoint that is either outside the PostIncLoop
// or dominated by IVIncInsertPos.
if (isa<Instruction>(Result) &&
&*Builder.GetInsertPoint())) {
// The induction variable's postinc expansion does not dominate this use.
// IVUsers tries to prevent this case, so it is rare. However, it can
// happen when an IVUser outside the loop is not dominated by the latch
// block. Adjusting IVIncInsertPos before expansion begins cannot handle
// all cases. Consider a phi outside whose operand is replaced during
// expansion with the value of the postinc user. Without fundamentally
// changing the way postinc users are tracked, the only remedy is
// inserting an extra IV increment. StepV might fold into PostLoopOffset,
// but hopefully expandCodeFor handles that.
bool useSubtract =
!ExpandTy->isPointerTy() && Step->isNonConstantNegative();
if (useSubtract)
Step = SE.getNegativeSCEV(Step);
Value *StepV;
// Expand the step somewhere that dominates the loop header.
SCEVInsertPointGuard Guard(Builder, this);
StepV = expandCodeFor(Step, IntTy, &L->getHeader()->front());
Result = expandIVInc(PN, StepV, L, ExpandTy, IntTy, useSubtract);
// We have decided to reuse an induction variable of a dominating loop. Apply
// truncation and/or inversion of the step.
if (TruncTy) {
Type *ResTy = Result->getType();
// Normalize the result type.
if (ResTy != SE.getEffectiveSCEVType(ResTy))
Result = InsertNoopCastOfTo(Result, SE.getEffectiveSCEVType(ResTy));
// Truncate the result.
if (TruncTy != Result->getType()) {
Result = Builder.CreateTrunc(Result, TruncTy);
// Invert the result.
if (InvertStep) {
Result = Builder.CreateSub(expandCodeFor(Normalized->getStart(), TruncTy),
// Re-apply any non-loop-dominating scale.
if (PostLoopScale) {
assert(S->isAffine() && "Can't linearly scale non-affine recurrences.");
Result = InsertNoopCastOfTo(Result, IntTy);
Result = Builder.CreateMul(Result,
expandCodeFor(PostLoopScale, IntTy));
// Re-apply any non-loop-dominating offset.
if (PostLoopOffset) {
if (PointerType *PTy = dyn_cast<PointerType>(ExpandTy)) {
if (Result->getType()->isIntegerTy()) {
Value *Base = expandCodeFor(PostLoopOffset, ExpandTy);
Result = expandAddToGEP(SE.getUnknown(Result), PTy, IntTy, Base);
} else {
Result = expandAddToGEP(PostLoopOffset, PTy, IntTy, Result);
} else {
Result = InsertNoopCastOfTo(Result, IntTy);
Result = Builder.CreateAdd(Result,
expandCodeFor(PostLoopOffset, IntTy));
return Result;
Value *SCEVExpander::visitAddRecExpr(const SCEVAddRecExpr *S) {
if (!CanonicalMode) return expandAddRecExprLiterally(S);
Type *Ty = SE.getEffectiveSCEVType(S->getType());
const Loop *L = S->getLoop();
// First check for an existing canonical IV in a suitable type.
PHINode *CanonicalIV = nullptr;
if (PHINode *PN = L->getCanonicalInductionVariable())
if (SE.getTypeSizeInBits(PN->getType()) >= SE.getTypeSizeInBits(Ty))
CanonicalIV = PN;
// Rewrite an AddRec in terms of the canonical induction variable, if
// its type is more narrow.
if (CanonicalIV &&
SE.getTypeSizeInBits(CanonicalIV->getType()) >
SE.getTypeSizeInBits(Ty)) {
SmallVector<const SCEV *, 4> NewOps(S->getNumOperands());
for (unsigned i = 0, e = S->getNumOperands(); i != e; ++i)
NewOps[i] = SE.getAnyExtendExpr(S->op_begin()[i], CanonicalIV->getType());
Value *V = expand(SE.getAddRecExpr(NewOps, S->getLoop(),
BasicBlock::iterator NewInsertPt =
findInsertPointAfter(cast<Instruction>(V), Builder.GetInsertBlock());
V = expandCodeFor(SE.getTruncateExpr(SE.getUnknown(V), Ty), nullptr,
return V;
// {X,+,F} --> X + {0,+,F}
if (!S->getStart()->isZero()) {
SmallVector<const SCEV *, 4> NewOps(S->op_begin(), S->op_end());
NewOps[0] = SE.getConstant(Ty, 0);
const SCEV *Rest = SE.getAddRecExpr(NewOps, L,
// Turn things like ptrtoint+arithmetic+inttoptr into GEP. See the
// comments on expandAddToGEP for details.
const SCEV *Base = S->getStart();
// Dig into the expression to find the pointer base for a GEP.
const SCEV *ExposedRest = Rest;
ExposePointerBase(Base, ExposedRest, SE);
// If we found a pointer, expand the AddRec with a GEP.
if (PointerType *PTy = dyn_cast<PointerType>(Base->getType())) {
// Make sure the Base isn't something exotic, such as a multiplied
// or divided pointer value. In those cases, the result type isn't
// actually a pointer type.
if (!isa<SCEVMulExpr>(Base) && !isa<SCEVUDivExpr>(Base)) {
Value *StartV = expand(Base);
assert(StartV->getType() == PTy && "Pointer type mismatch for GEP!");
return expandAddToGEP(ExposedRest, PTy, Ty, StartV);
// Just do a normal add. Pre-expand the operands to suppress folding.
// The LHS and RHS values are factored out of the expand call to make the
// output independent of the argument evaluation order.
const SCEV *AddExprLHS = SE.getUnknown(expand(S->getStart()));
const SCEV *AddExprRHS = SE.getUnknown(expand(Rest));
return expand(SE.getAddExpr(AddExprLHS, AddExprRHS));
// If we don't yet have a canonical IV, create one.
if (!CanonicalIV) {
// Create and insert the PHI node for the induction variable in the
// specified loop.
BasicBlock *Header = L->getHeader();
pred_iterator HPB = pred_begin(Header), HPE = pred_end(Header);
CanonicalIV = PHINode::Create(Ty, std::distance(HPB, HPE), "indvar",
SmallSet<BasicBlock *, 4> PredSeen;
Constant *One = ConstantInt::get(Ty, 1);
for (pred_iterator HPI = HPB; HPI != HPE; ++HPI) {
BasicBlock *HP = *HPI;
if (!PredSeen.insert(HP).second) {
// There must be an incoming value for each predecessor, even the
// duplicates!
CanonicalIV->addIncoming(CanonicalIV->getIncomingValueForBlock(HP), HP);
if (L->contains(HP)) {
// Insert a unit add instruction right before the terminator
// corresponding to the back-edge.
Instruction *Add = BinaryOperator::CreateAdd(CanonicalIV, One,
CanonicalIV->addIncoming(Add, HP);
} else {
CanonicalIV->addIncoming(Constant::getNullValue(Ty), HP);
// {0,+,1} --> Insert a canonical induction variable into the loop!
if (S->isAffine() && S->getOperand(1)->isOne()) {
assert(Ty == SE.getEffectiveSCEVType(CanonicalIV->getType()) &&
"IVs with types different from the canonical IV should "
"already have been handled!");
return CanonicalIV;
// {0,+,F} --> {0,+,1} * F
// If this is a simple linear addrec, emit it now as a special case.
if (S->isAffine()) // {0,+,F} --> i*F
// If this is a chain of recurrences, turn it into a closed form, using the
// folders, then expandCodeFor the closed form. This allows the folders to
// simplify the expression without having to build a bunch of special code
// into this folder.
const SCEV *IH = SE.getUnknown(CanonicalIV); // Get I as a "symbolic" SCEV.
// Promote S up to the canonical IV type, if the cast is foldable.
const SCEV *NewS = S;
const SCEV *Ext = SE.getNoopOrAnyExtend(S, CanonicalIV->getType());
if (isa<SCEVAddRecExpr>(Ext))
NewS = Ext;
const SCEV *V = cast<SCEVAddRecExpr>(NewS)->evaluateAtIteration(IH, SE);
//cerr << "Evaluated: " << *this << "\n to: " << *V << "\n";
// Truncate the result down to the original type, if needed.
const SCEV *T = SE.getTruncateOrNoop(V, Ty);
return expand(T);
Value *SCEVExpander::visitTruncateExpr(const SCEVTruncateExpr *S) {
Type *Ty = SE.getEffectiveSCEVType(S->getType());
Value *V = expandCodeFor(S->getOperand(),
Value *I = Builder.CreateTrunc(V, Ty);
return I;
Value *SCEVExpander::visitZeroExtendExpr(const SCEVZeroExtendExpr *S) {
Type *Ty = SE.getEffectiveSCEVType(S->getType());
Value *V = expandCodeFor(S->getOperand(),
Value *I = Builder.CreateZExt(V, Ty);
return I;
Value *SCEVExpander::visitSignExtendExpr(const SCEVSignExtendExpr *S) {
Type *Ty = SE.getEffectiveSCEVType(S->getType());
Value *V = expandCodeFor(S->getOperand(),
Value *I = Builder.CreateSExt(V, Ty);
return I;
Value *SCEVExpander::visitSMaxExpr(const SCEVSMaxExpr *S) {
Value *LHS = expand(S->getOperand(S->getNumOperands()-1));
Type *Ty = LHS->getType();
for (int i = S->getNumOperands()-2; i >= 0; --i) {
// In the case of mixed integer and pointer types, do the
// rest of the comparisons as integer.
if (S->getOperand(i)->getType() != Ty) {
Ty = SE.getEffectiveSCEVType(Ty);
LHS = InsertNoopCastOfTo(LHS, Ty);
Value *RHS = expandCodeFor(S->getOperand(i), Ty);
Value *ICmp = Builder.CreateICmpSGT(LHS, RHS);
Value *Sel = Builder.CreateSelect(ICmp, LHS, RHS, "smax");
LHS = Sel;
// In the case of mixed integer and pointer types, cast the
// final result back to the pointer type.
if (LHS->getType() != S->getType())
LHS = InsertNoopCastOfTo(LHS, S->getType());
return LHS;
Value *SCEVExpander::visitUMaxExpr(const SCEVUMaxExpr *S) {
Value *LHS = expand(S->getOperand(S->getNumOperands()-1));
Type *Ty = LHS->getType();
for (int i = S->getNumOperands()-2; i >= 0; --i) {
// In the case of mixed integer and pointer types, do the
// rest of the comparisons as integer.
if (S->getOperand(i)->getType() != Ty) {
Ty = SE.getEffectiveSCEVType(Ty);
LHS = InsertNoopCastOfTo(LHS, Ty);
Value *RHS = expandCodeFor(S->getOperand(i), Ty);
Value *ICmp = Builder.CreateICmpUGT(LHS, RHS);
Value *Sel = Builder.CreateSelect(ICmp, LHS, RHS, "umax");
LHS = Sel;
// In the case of mixed integer and pointer types, cast the
// final result back to the pointer type.
if (LHS->getType() != S->getType())
LHS = InsertNoopCastOfTo(LHS, S->getType());
return LHS;
Value *SCEVExpander::expandCodeFor(const SCEV *SH, Type *Ty,
Instruction *IP) {
return expandCodeFor(SH, Ty);
Value *SCEVExpander::expandCodeFor(const SCEV *SH, Type *Ty) {
// Expand the code for this SCEV.
Value *V = expand(SH);
if (Ty) {
assert(SE.getTypeSizeInBits(Ty) == SE.getTypeSizeInBits(SH->getType()) &&
"non-trivial casts should be done with the SCEVs directly!");
V = InsertNoopCastOfTo(V, Ty);
return V;
SCEVExpander::FindValueInExprValueMap(const SCEV *S,
const Instruction *InsertPt) {
SetVector<ScalarEvolution::ValueOffsetPair> *Set = SE.getSCEVValues(S);
// If the expansion is not in CanonicalMode, and the SCEV contains any
// sub scAddRecExpr type SCEV, it is required to expand the SCEV literally.
if (CanonicalMode || !SE.containsAddRecurrence(S)) {
// If S is scConstant, it may be worse to reuse an existing Value.
if (S->getSCEVType() != scConstant && Set) {
// Choose a Value from the set which dominates the insertPt.
// insertPt should be inside the Value's parent loop so as not to break
// the LCSSA form.
for (auto const &VOPair : *Set) {
Value *V = VOPair.first;
ConstantInt *Offset = VOPair.second;
Instruction *EntInst = nullptr;
if (V && isa<Instruction>(V) && (EntInst = cast<Instruction>(V)) &&
S->getType() == V->getType() &&
EntInst->getFunction() == InsertPt->getFunction() &&
SE.DT.dominates(EntInst, InsertPt) &&
(SE.LI.getLoopFor(EntInst->getParent()) == nullptr ||
return {V, Offset};
return {nullptr, nullptr};
// The expansion of SCEV will either reuse a previous Value in ExprValueMap,
// or expand the SCEV literally. Specifically, if the expansion is in LSRMode,
// and the SCEV contains any sub scAddRecExpr type SCEV, it will be expanded
// literally, to prevent LSR's transformed SCEV from being reverted. Otherwise,
// the expansion will try to reuse Value from ExprValueMap, and only when it
// fails, expand the SCEV literally.
Value *SCEVExpander::expand(const SCEV *S) {
// Compute an insertion point for this SCEV object. Hoist the instructions
// as far out in the loop nest as possible.
Instruction *InsertPt = &*Builder.GetInsertPoint();
for (Loop *L = SE.LI.getLoopFor(Builder.GetInsertBlock());;
L = L->getParentLoop())
if (SE.isLoopInvariant(S, L)) {
if (!L) break;
if (BasicBlock *Preheader = L->getLoopPreheader())
InsertPt = Preheader->getTerminator();
else {
// LSR sets the insertion point for AddRec start/step values to the
// block start to simplify value reuse, even though it's an invalid
// position. SCEVExpander must correct for this in all cases.
InsertPt = &*L->getHeader()->getFirstInsertionPt();
} else {
// We can move insertion point only if there is no div or rem operations
// otherwise we are risky to move it over the check for zero denominator.
auto SafeToHoist = [](const SCEV *S) {
return !SCEVExprContains(S, [](const SCEV *S) {
if (const auto *D = dyn_cast<SCEVUDivExpr>(S)) {
if (const auto *SC = dyn_cast<SCEVConstant>(D->getRHS()))
// Division by non-zero constants can be hoisted.
return SC->getValue()->isZero();
// All other divisions should not be moved as they may be
// divisions by zero and should be kept within the
// conditions of the surrounding loops that guard their
// execution (see PR35406).
return true;
return false;
// If the SCEV is computable at this level, insert it into the header
// after the PHIs (and after any other instructions that we've inserted
// there) so that it is guaranteed to dominate any user inside the loop.
if (L && SE.hasComputableLoopEvolution(S, L) && !PostIncLoops.count(L) &&
InsertPt = &*L->getHeader()->getFirstInsertionPt();
while (InsertPt->getIterator() != Builder.GetInsertPoint() &&
(isInsertedInstruction(InsertPt) ||
isa<DbgInfoIntrinsic>(InsertPt))) {
InsertPt = &*std::next(InsertPt->getIterator());
// Check to see if we already expanded this here.
auto I = InsertedExpressions.find(std::make_pair(S, InsertPt));
if (I != InsertedExpressions.end())
return I->second;
SCEVInsertPointGuard Guard(Builder, this);
// Expand the expression into instructions.
ScalarEvolution::ValueOffsetPair VO = FindValueInExprValueMap(S, InsertPt);
Value *V = VO.first;
if (!V)
V = visit(S);
else if (VO.second) {
if (PointerType *Vty = dyn_cast<PointerType>(V->getType())) {
Type *Ety = Vty->getPointerElementType();
int64_t Offset = VO.second->getSExtValue();
int64_t ESize = SE.getTypeSizeInBits(Ety);
if ((Offset * 8) % ESize == 0) {
ConstantInt *Idx =
ConstantInt::getSigned(VO.second->getType(), -(Offset * 8) / ESize);
V = Builder.CreateGEP(Ety, V, Idx, "scevgep");
} else {
ConstantInt *Idx =
ConstantInt::getSigned(VO.second->getType(), -Offset);
unsigned AS = Vty->getAddressSpace();
V = Builder.CreateBitCast(V, Type::getInt8PtrTy(SE.getContext(), AS));
V = Builder.CreateGEP(Type::getInt8Ty(SE.getContext()), V, Idx,
V = Builder.CreateBitCast(V, Vty);
} else {
V = Builder.CreateSub(V, VO.second);
// Remember the expanded value for this SCEV at this location.
// This is independent of PostIncLoops. The mapped value simply materializes
// the expression at this insertion point. If the mapped value happened to be
// a postinc expansion, it could be reused by a non-postinc user, but only if
// its insertion point was already at the head of the loop.
InsertedExpressions[std::make_pair(S, InsertPt)] = V;
return V;
void SCEVExpander::rememberInstruction(Value *I) {
if (!PostIncLoops.empty())
/// getOrInsertCanonicalInductionVariable - This method returns the
/// canonical induction variable of the specified type for the specified
/// loop (inserting one if there is none). A canonical induction variable
/// starts at zero and steps by one on each iteration.
PHINode *
SCEVExpander::getOrInsertCanonicalInductionVariable(const Loop *L,
Type *Ty) {
assert(Ty->isIntegerTy() && "Can only insert integer induction variables!");
// Build a SCEV for {0,+,1}<L>.
// Conservatively use FlagAnyWrap for now.
const SCEV *H = SE.getAddRecExpr(SE.getConstant(Ty, 0),
SE.getConstant(Ty, 1), L, SCEV::FlagAnyWrap);
// Emit code for it.
SCEVInsertPointGuard Guard(Builder, this);
PHINode *V =
cast<PHINode>(expandCodeFor(H, nullptr, &L->getHeader()->front()));
return V;
/// replaceCongruentIVs - Check for congruent phis in this loop header and
/// replace them with their most canonical representative. Return the number of
/// phis eliminated.
/// This does not depend on any SCEVExpander state but should be used in
/// the same context that SCEVExpander is used.
SCEVExpander::replaceCongruentIVs(Loop *L, const DominatorTree *DT,
SmallVectorImpl<WeakTrackingVH> &DeadInsts,
const TargetTransformInfo *TTI) {
// Find integer phis in order of increasing width.
SmallVector<PHINode*, 8> Phis;
for (PHINode &PN : L->getHeader()->phis())
if (TTI)
llvm::sort(Phis.begin(), Phis.end(), [](Value *LHS, Value *RHS) {
// Put pointers at the back and make sure pointer < pointer = false.
if (!LHS->getType()->isIntegerTy() || !RHS->getType()->isIntegerTy())
return RHS->getType()->isIntegerTy() && !LHS->getType()->isIntegerTy();
return RHS->getType()->getPrimitiveSizeInBits() <
unsigned NumElim = 0;
DenseMap<const SCEV *, PHINode *> ExprToIVMap;
// Process phis from wide to narrow. Map wide phis to their truncation
// so narrow phis can reuse them.
for (PHINode *Phi : Phis) {
auto SimplifyPHINode = [&](PHINode *PN) -> Value * {
if (Value *V = SimplifyInstruction(PN, {DL, &SE.TLI, &SE.DT, &SE.AC}))
return V;
if (!SE.isSCEVable(PN->getType()))
return nullptr;
auto *Const = dyn_cast<SCEVConstant>(SE.getSCEV(PN));
if (!Const)
return nullptr;
return Const->getValue();
// Fold constant phis. They may be congruent to other constant phis and
// would confuse the logic below that expects proper IVs.
if (Value *V = SimplifyPHINode(Phi)) {
if (V->getType() != Phi->getType())
DEBUG_WITH_TYPE(DebugType, dbgs()
<< "INDVARS: Eliminated constant iv: " << *Phi << '\n');
if (!SE.isSCEVable(Phi->getType()))
PHINode *&OrigPhiRef = ExprToIVMap[SE.getSCEV(Phi)];
if (!OrigPhiRef) {
OrigPhiRef = Phi;
if (Phi->getType()->isIntegerTy() && TTI &&
TTI->isTruncateFree(Phi->getType(), Phis.back()->getType())) {
// This phi can be freely truncated to the narrowest phi type. Map the
// truncated expression to it so it will be reused for narrow types.
const SCEV *TruncExpr =
SE.getTruncateExpr(SE.getSCEV(Phi), Phis.back()->getType());
ExprToIVMap[TruncExpr] = Phi;
// Replacing a pointer phi with an integer phi or vice-versa doesn't make
// sense.
if (OrigPhiRef->getType()->isPointerTy() != Phi->getType()->isPointerTy())
if (BasicBlock *LatchBlock = L->getLoopLatch()) {
Instruction *OrigInc = dyn_cast<Instruction>(
Instruction *IsomorphicInc =
if (OrigInc && IsomorphicInc) {
// If this phi has the same width but is more canonical, replace the
// original with it. As part of the "more canonical" determination,
// respect a prior decision to use an IV chain.
if (OrigPhiRef->getType() == Phi->getType() &&
!(ChainedPhis.count(Phi) ||
isExpandedAddRecExprPHI(OrigPhiRef, OrigInc, L)) &&
(ChainedPhis.count(Phi) ||
isExpandedAddRecExprPHI(Phi, IsomorphicInc, L))) {
std::swap(OrigPhiRef, Phi);
std::swap(OrigInc, IsomorphicInc);
// Replacing the congruent phi is sufficient because acyclic
// redundancy elimination, CSE/GVN, should handle the
// rest. However, once SCEV proves that a phi is congruent,
// it's often the head of an IV user cycle that is isomorphic
// with the original phi. It's worth eagerly cleaning up the
// common case of a single IV increment so that DeleteDeadPHIs
// can remove cycles that had postinc uses.
const SCEV *TruncExpr =
SE.getTruncateOrNoop(SE.getSCEV(OrigInc), IsomorphicInc->getType());
if (OrigInc != IsomorphicInc &&
TruncExpr == SE.getSCEV(IsomorphicInc) &&
SE.LI.replacementPreservesLCSSAForm(IsomorphicInc, OrigInc) &&
hoistIVInc(OrigInc, IsomorphicInc)) {
dbgs() << "INDVARS: Eliminated congruent "
<< *IsomorphicInc << '\n');
Value *NewInc = OrigInc;
if (OrigInc->getType() != IsomorphicInc->getType()) {
Instruction *IP = nullptr;
if (PHINode *PN = dyn_cast<PHINode>(OrigInc))
IP = &*PN->getParent()->getFirstInsertionPt();
IP = OrigInc->getNextNode();
IRBuilder<> Builder(IP);
NewInc = Builder.CreateTruncOrBitCast(
OrigInc, IsomorphicInc->getType(), IVName);
DEBUG_WITH_TYPE(DebugType, dbgs() << "INDVARS: Eliminated congruent iv: "
<< *Phi << '\n');
Value *NewIV = OrigPhiRef;
if (OrigPhiRef->getType() != Phi->getType()) {
IRBuilder<> Builder(&*L->getHeader()->getFirstInsertionPt());
NewIV = Builder.CreateTruncOrBitCast(OrigPhiRef, Phi->getType(), IVName);
return NumElim;
Value *SCEVExpander::getExactExistingExpansion(const SCEV *S,
const Instruction *At, Loop *L) {
Optional<ScalarEvolution::ValueOffsetPair> VO =
getRelatedExistingExpansion(S, At, L);
if (VO && VO.getValue().second == nullptr)
return VO.getValue().first;
return nullptr;
SCEVExpander::getRelatedExistingExpansion(const SCEV *S, const Instruction *At,
Loop *L) {
using namespace llvm::PatternMatch;
SmallVector<BasicBlock *, 4> ExitingBlocks;
// Look for suitable value in simple conditions at the loop exits.
for (BasicBlock *BB : ExitingBlocks) {
ICmpInst::Predicate Pred;
Instruction *LHS, *RHS;
BasicBlock *TrueBB, *FalseBB;
if (!match(BB->getTerminator(),
m_Br(m_ICmp(Pred, m_Instruction(LHS), m_Instruction(RHS)),
TrueBB, FalseBB)))
if (SE.getSCEV(LHS) == S && SE.DT.dominates(LHS, At))
return ScalarEvolution::ValueOffsetPair(LHS, nullptr);
if (SE.getSCEV(RHS) == S && SE.DT.dominates(RHS, At))
return ScalarEvolution::ValueOffsetPair(RHS, nullptr);
// Use expand's logic which is used for reusing a previous Value in
// ExprValueMap.
ScalarEvolution::ValueOffsetPair VO = FindValueInExprValueMap(S, At);
if (VO.first)
return VO;
// There is potential to make this significantly smarter, but this simple
// heuristic already gets some interesting cases.
// Can not find suitable value.
return None;
bool SCEVExpander::isHighCostExpansionHelper(
const SCEV *S, Loop *L, const Instruction *At,
SmallPtrSetImpl<const SCEV *> &Processed) {
// If we can find an existing value for this scev available at the point "At"
// then consider the expression cheap.
if (At && getRelatedExistingExpansion(S, At, L))
return false;
// Zero/One operand expressions
switch (S->getSCEVType()) {
case scUnknown:
case scConstant:
return false;
case scTruncate:
return isHighCostExpansionHelper(cast<SCEVTruncateExpr>(S)->getOperand(),
L, At, Processed);
case scZeroExtend:
return isHighCostExpansionHelper(cast<SCEVZeroExtendExpr>(S)->getOperand(),
L, At, Processed);
case scSignExtend:
return isHighCostExpansionHelper(cast<SCEVSignExtendExpr>(S)->getOperand(),
L, At, Processed);
if (!Processed.insert(S).second)
return false;
if (auto *UDivExpr = dyn_cast<SCEVUDivExpr>(S)) {
// If the divisor is a power of two and the SCEV type fits in a native
// integer, consider the division cheap irrespective of whether it occurs in
// the user code since it can be lowered into a right shift.
if (auto *SC = dyn_cast<SCEVConstant>(UDivExpr->getRHS()))
if (SC->getAPInt().isPowerOf2()) {
const DataLayout &DL =
unsigned Width = cast<IntegerType>(UDivExpr->getType())->getBitWidth();
return DL.isIllegalInteger(Width);
// UDivExpr is very likely a UDiv that ScalarEvolution's HowFarToZero or
// HowManyLessThans produced to compute a precise expression, rather than a
// UDiv from the user's code. If we can't find a UDiv in the code with some
// simple searching, assume the former consider UDivExpr expensive to
// compute.
BasicBlock *ExitingBB = L->getExitingBlock();
if (!ExitingBB)
return true;
// At the beginning of this function we already tried to find existing value
// for plain 'S'. Now try to lookup 'S + 1' since it is common pattern
// involving division. This is just a simple search heuristic.
if (!At)
At = &ExitingBB->back();
if (!getRelatedExistingExpansion(
SE.getAddExpr(S, SE.getConstant(S->getType(), 1)), At, L))
return true;
// HowManyLessThans uses a Max expression whenever the loop is not guarded by
// the exit condition.
if (isa<SCEVSMaxExpr>(S) || isa<SCEVUMaxExpr>(S))
return true;
// Recurse past nary expressions, which commonly occur in the
// BackedgeTakenCount. They may already exist in program code, and if not,
// they are not too expensive rematerialize.
if (const SCEVNAryExpr *NAry = dyn_cast<SCEVNAryExpr>(S)) {
for (auto *Op : NAry->operands())
if (isHighCostExpansionHelper(Op, L, At, Processed))
return true;
// If we haven't recognized an expensive SCEV pattern, assume it's an
// expression produced by program code.
return false;
Value *SCEVExpander::expandCodeForPredicate(const SCEVPredicate *Pred,
Instruction *IP) {
switch (Pred->getKind()) {
case SCEVPredicate::P_Union:
return expandUnionPredicate(cast<SCEVUnionPredicate>(Pred), IP);
case SCEVPredicate::P_Equal:
return expandEqualPredicate(cast<SCEVEqualPredicate>(Pred), IP);
case SCEVPredicate::P_Wrap: {
auto *AddRecPred = cast<SCEVWrapPredicate>(Pred);
return expandWrapPredicate(AddRecPred, IP);
llvm_unreachable("Unknown SCEV predicate type");
Value *SCEVExpander::expandEqualPredicate(const SCEVEqualPredicate *Pred,
Instruction *IP) {
Value *Expr0 = expandCodeFor(Pred->getLHS(), Pred->getLHS()->getType(), IP);
Value *Expr1 = expandCodeFor(Pred->getRHS(), Pred->getRHS()->getType(), IP);
auto *I = Builder.CreateICmpNE(Expr0, Expr1, "ident.check");
return I;
Value *SCEVExpander::generateOverflowCheck(const SCEVAddRecExpr *AR,
Instruction *Loc, bool Signed) {
assert(AR->isAffine() && "Cannot generate RT check for "
"non-affine expression");
SCEVUnionPredicate Pred;
const SCEV *ExitCount =
SE.getPredicatedBackedgeTakenCount(AR->getLoop(), Pred);
assert(ExitCount != SE.getCouldNotCompute() && "Invalid loop count");
const SCEV *Step = AR->getStepRecurrence(SE);
const SCEV *Start = AR->getStart();
Type *ARTy = AR->getType();
unsigned SrcBits = SE.getTypeSizeInBits(ExitCount->getType());
unsigned DstBits = SE.getTypeSizeInBits(ARTy);
// The expression {Start,+,Step} has nusw/nssw if
// Step < 0, Start - |Step| * Backedge <= Start
// Step >= 0, Start + |Step| * Backedge > Start
// and |Step| * Backedge doesn't unsigned overflow.
IntegerType *CountTy = IntegerType::get(Loc->getContext(), SrcBits);
Value *TripCountVal = expandCodeFor(ExitCount, CountTy, Loc);
IntegerType *Ty =
IntegerType::get(Loc->getContext(), SE.getTypeSizeInBits(ARTy));
Type *ARExpandTy = DL.isNonIntegralPointerType(ARTy) ? ARTy : Ty;
Value *StepValue = expandCodeFor(Step, Ty, Loc);
Value *NegStepValue = expandCodeFor(SE.getNegativeSCEV(Step), Ty, Loc);
Value *StartValue = expandCodeFor(Start, ARExpandTy, Loc);
ConstantInt *Zero =
ConstantInt::get(Loc->getContext(), APInt::getNullValue(DstBits));
// Compute |Step|
Value *StepCompare = Builder.CreateICmp(ICmpInst::ICMP_SLT, StepValue, Zero);
Value *AbsStep = Builder.CreateSelect(StepCompare, NegStepValue, StepValue);
// Get the backedge taken count and truncate or extended to the AR type.
Value *TruncTripCount = Builder.CreateZExtOrTrunc(TripCountVal, Ty);
auto *MulF = Intrinsic::getDeclaration(Loc->getModule(),
Intrinsic::umul_with_overflow, Ty);
// Compute |Step| * Backedge
CallInst *Mul = Builder.CreateCall(MulF, {AbsStep, TruncTripCount}, "mul");
Value *MulV = Builder.CreateExtractValue(Mul, 0, "mul.result");
Value *OfMul = Builder.CreateExtractValue(Mul, 1, "mul.overflow");
// Compute:
// Start + |Step| * Backedge < Start
// Start - |Step| * Backedge > Start
Value *Add = nullptr, *Sub = nullptr;
if (PointerType *ARPtrTy = dyn_cast<PointerType>(ARExpandTy)) {
const SCEV *MulS = SE.getSCEV(MulV);
const SCEV *NegMulS = SE.getNegativeSCEV(MulS);
Add = Builder.CreateBitCast(expandAddToGEP(MulS, ARPtrTy, Ty, StartValue),
Sub = Builder.CreateBitCast(
expandAddToGEP(NegMulS, ARPtrTy, Ty, StartValue), ARPtrTy);
} else {
Add = Builder.CreateAdd(StartValue, MulV);
Sub = Builder.CreateSub(StartValue, MulV);
Value *EndCompareGT = Builder.CreateICmp(
Signed ? ICmpInst::ICMP_SGT : ICmpInst::ICMP_UGT, Sub, StartValue);
Value *EndCompareLT = Builder.CreateICmp(
Signed ? ICmpInst::ICMP_SLT : ICmpInst::ICMP_ULT, Add, StartValue);
// Select the answer based on the sign of Step.
Value *EndCheck =
Builder.CreateSelect(StepCompare, EndCompareGT, EndCompareLT);
// If the backedge taken count type is larger than the AR type,
// check that we don't drop any bits by truncating it. If we are
// dropping bits, then we have overflow (unless the step is zero).
if (SE.getTypeSizeInBits(CountTy) > SE.getTypeSizeInBits(Ty)) {
auto MaxVal = APInt::getMaxValue(DstBits).zext(SrcBits);
auto *BackedgeCheck =
Builder.CreateICmp(ICmpInst::ICMP_UGT, TripCountVal,
ConstantInt::get(Loc->getContext(), MaxVal));
BackedgeCheck = Builder.CreateAnd(
BackedgeCheck, Builder.CreateICmp(ICmpInst::ICMP_NE, StepValue, Zero));
EndCheck = Builder.CreateOr(EndCheck, BackedgeCheck);
EndCheck = Builder.CreateOr(EndCheck, OfMul);
return EndCheck;
Value *SCEVExpander::expandWrapPredicate(const SCEVWrapPredicate *Pred,
Instruction *IP) {
const auto *A = cast<SCEVAddRecExpr>(Pred->getExpr());
Value *NSSWCheck = nullptr, *NUSWCheck = nullptr;
// Add a check for NUSW
if (Pred->getFlags() & SCEVWrapPredicate::IncrementNUSW)
NUSWCheck = generateOverflowCheck(A, IP, false);
// Add a check for NSSW
if (Pred->getFlags() & SCEVWrapPredicate::IncrementNSSW)
NSSWCheck = generateOverflowCheck(A, IP, true);
if (NUSWCheck && NSSWCheck)
return Builder.CreateOr(NUSWCheck, NSSWCheck);
if (NUSWCheck)
return NUSWCheck;
if (NSSWCheck)
return NSSWCheck;
return ConstantInt::getFalse(IP->getContext());
Value *SCEVExpander::expandUnionPredicate(const SCEVUnionPredicate *Union,
Instruction *IP) {
auto *BoolType = IntegerType::get(IP->getContext(), 1);
Value *Check = ConstantInt::getNullValue(BoolType);
// Loop over all checks in this set.
for (auto Pred : Union->getPredicates()) {
auto *NextCheck = expandCodeForPredicate(Pred, IP);
Check = Builder.CreateOr(Check, NextCheck);
return Check;
namespace {
// Search for a SCEV subexpression that is not safe to expand. Any expression
// that may expand to a !isSafeToSpeculativelyExecute value is unsafe, namely
// UDiv expressions. We don't know if the UDiv is derived from an IR divide
// instruction, but the important thing is that we prove the denominator is
// nonzero before expansion.
// IVUsers already checks that IV-derived expressions are safe. So this check is
// only needed when the expression includes some subexpression that is not IV
// derived.
// Currently, we only allow division by a nonzero constant here. If this is
// inadequate, we could easily allow division by SCEVUnknown by using
// ValueTracking to check isKnownNonZero().
// We cannot generally expand recurrences unless the step dominates the loop
// header. The expander handles the special case of affine recurrences by
// scaling the recurrence outside the loop, but this technique isn't generally
// applicable. Expanding a nested recurrence outside a loop requires computing
// binomial coefficients. This could be done, but the recurrence has to be in a
// perfectly reduced form, which can't be guaranteed.
struct SCEVFindUnsafe {
ScalarEvolution &SE;
bool IsUnsafe;
SCEVFindUnsafe(ScalarEvolution &se): SE(se), IsUnsafe(false) {}
bool follow(const SCEV *S) {
if (const SCEVUDivExpr *D = dyn_cast<SCEVUDivExpr>(S)) {
const SCEVConstant *SC = dyn_cast<SCEVConstant>(D->getRHS());
if (!SC || SC->getValue()->isZero()) {
IsUnsafe = true;
return false;
if (const SCEVAddRecExpr *AR = dyn_cast<SCEVAddRecExpr>(S)) {
const SCEV *Step = AR->getStepRecurrence(SE);
if (!AR->isAffine() && !SE.dominates(Step, AR->getLoop()->getHeader())) {
IsUnsafe = true;
return false;
return true;
bool isDone() const { return IsUnsafe; }
namespace llvm {
bool isSafeToExpand(const SCEV *S, ScalarEvolution &SE) {
SCEVFindUnsafe Search(SE);
visitAll(S, Search);
return !Search.IsUnsafe;
bool isSafeToExpandAt(const SCEV *S, const Instruction *InsertionPoint,
ScalarEvolution &SE) {
return isSafeToExpand(S, SE) && SE.dominates(S, InsertionPoint->getParent());